WASHINGTON — More than half a million consumers have received a total of $45.8 billion in aid from the five largest banks as part of a national mortgage settlement struck last year between big banks and state and federal officials, the monitor of the agreement reported Thursday.

The figures are for assistance from March 1 through Dec. 31 and include trial reductions in mortgage payments that had not been converted into permanent modifications, according to the Office of Mortgage Settlement Oversight.

"I believe we have made progress, particularly as it relates to consumer relief, but I know from my regular conversations with advocates across the nation that the banks and I have much more work to do on behalf of borrowers," said Joseph A. Smith Jr., a former North Carolina banking commissioner who is serving as the deal's monitor.

The relief is part of a settlement that was struck a year ago by 49 state attorneys general, several federal agencies and the nation's five largest mortgage servicers — Bank of America Corp., JPMorgan Chase & Co., Wells Fargo & Co., Citigroup Inc. and Ally Financial Inc.

Under the $25 billion settlement, servicers were required to provide $20 billion in relief to consumers, with different types of relief getting different amounts of credit toward that figure.

Because the servicers get less than a dollar's worth of credit for each dollar in relief, consumers have received more than $20 billion in relief. A separate $5 billion under the agreement went to states, primarily for foreclosure prevention programs.

The settlement resolved investigations into allegations the financial institutions had used flawed paperwork and other faulty practices to foreclose on homes.

Much of the aid to consumers has been through short sales — about $20 billion nationally. So far only Ally has met its obligation under the settlement, the monitor said.

The other four banks had much larger obligations.

Bank of America had provided the most relief as of Dec. 31 — $26.8 billion to 318,024 borrowers. Bank of America said Thursday it was on track to meet its obligations under the settlement by the end of March.